A radar signal sorting method, program, device, and storage medium based on improved sparse subspace clustering.

Abstract

This invention belongs to the field of radar signal sorting technology, specifically relating to a radar signal sorting method, program, device, and storage medium based on improved sparse subspace clustering. This invention constructs a complex network of radar pulse sequences based on the self-representation properties between radar pulse data points in the same subspace. It utilizes a generalized orthogonal matching pursuit algorithm to reduce the number of connections between pulses from different radars in the complex network, thereby reducing computational complexity. Borrowing the idea of ​​graph segmentation, it uses Laplace spectral decomposition to mine the geometric correlations of radar pulse signals from the same source, achieving efficient sorting of non-ideal radar signals under complex electromagnetic environments. Simultaneously, this invention designs an algorithm based on an energy correction severance threshold, which can effectively solve for the accurate calculation of the number of cluster centers. This invention can effectively solve the problem of mis-sorting caused by aliasing or missing parameters of complex radar operating conditions.

Description

Technical Field

[0001] This invention belongs to the field of radar signal sorting technology, specifically relating to a radar signal sorting method, program, device, and storage medium based on improved sparse subspace clustering. Background Technology

[0002] The radar signal intercepted by the receiver can be viewed as a series of ordered radar pulses characterized by multidimensional state parameters. Only by filtering out pulse sequences belonging to the same radiation source from the intercepted randomly interleaved pulse stream can the various radiation source signals be "clearly seen" in time, further completing the radiation source target identification and implementing countermeasures. This reconnaissance process of separating the pulse stream into pulse sequences from different transmitters based on the correlation of characteristic parameters of signals from the same radiation source and the differences in characteristic parameters of signals from different radiation sources is called radar signal sorting.

[0003] Based on the selection of intercepted radar signal parameters, existing radar signal sorting methods can be mainly divided into two categories: single-parameter-based sorting and multi-parameter-based sorting. At the beginning of radar signal sorting algorithm research, since the pulse repetition interval (PRI) measurement was the most stable, researchers mainly used it as the key characteristic parameter for radar signal sorting. Published radar signal sorting methods based on single-parameter PRI can be roughly divided into four categories: differential histogram algorithms, PRI transform algorithms, sequence search algorithms, and period estimation algorithms. However, these methods are easily affected by PRI estimation errors, especially in complex electromagnetic environments where PRI jitter and loss are highly likely. Although recent PRI sorting algorithms have shown good adaptability to PRI jitter and loss, these algorithms cannot sort complex, intentionally modulated pulse signals.

[0004] With the increasing number and variety of radiation sources, researchers can no longer limit themselves to single-parameter sorting based on PRI (Primary Parameter) to improve radar signal sorting performance. Therefore, radar operating parameters such as Pulse Description Word (PDW) are used as the basis for sorting. Besides PRI, PDW includes carrier frequency (RF), pulse width (PW), pulse amplitude (PA), and direction of arrival (DOA). In the field of multi-parameter sorting, researchers mainly focus on the application and improvement of machine learning methods. Commonly used multi-parameter radar signal sorting algorithms can be divided into three categories: prototype clustering, density clustering, and deep learning clustering.

[0005] k-means is a typical algorithm for prototypical clustering sorting. Its basic idea is to calculate the distance relationships between multidimensional radar signals, iteratively determine cluster centers, and divide the signals into groups based on the nearest radar pulses. This algorithm can effectively sort mixed radar signals with high inter-cluster separation, but it is sensitive to the initial selection of cluster centers. In recent years, several improved k-means algorithms have been proposed. These algorithms are less affected by the initial cluster centers, but they are computationally intensive and unsuitable for practical applications. Furthermore, prototypical clustering sorting algorithms are very sensitive to radar signals with aliased parameters, and the probability of sorting errors in overlapping areas is high.

[0006] Density clustering algorithms determine cluster structure based on the density of sample distribution, using the number of points within a certain neighborhood as a connectivity criterion, and continuously expanding clusters based on this connectivity to obtain the final clustering result. While density clustering algorithms are insensitive to the initialization of cluster centers, inappropriate thresholds can lead to low robustness. In recent years, with the rapid development of deep learning, radar signal sorting based on deep neural networks (DNNs) has become a research hotspot, such as the relatively classic convolutional neural networks, autoencoders, and graph neural networks. This method achieves radar signal sorting through a data-driven approach, typically requiring a large number of labeled data samples to train the deep learning model to achieve good performance. This is severely limited in practical scenarios with few samples and requires significant computational costs.

[0007] The methods described above cannot be used to sort radar signals where radar state parameters are severely aliased in the PDW domain under non-ideal conditions. Therefore, the challenge of low inter-class separation and intra-class clustering of pulse sequences caused by aliasing and partial information loss in radar pulse signals intercepted under complex electromagnetic environments remains a key research focus in the field of radar signal sorting. Summary of the Invention

[0008] The purpose of this invention is to address the problem of low inter-class separation and intra-class clustering of radar pulse signals due to aliasing and partial information loss in complex electromagnetic environments, and to provide a radar signal sorting method, program, device and storage medium based on improved sparse subspace clustering.

[0009] A radar signal sorting method based on improved sparse subspace clustering includes the following steps:

[0010] Step 1: Obtain the time series X of multiple radar signal pulses, and use the self-representation properties between multi-state parameter pulse signals in the same subspace to represent the proximity relationship, that is, the spatial correlation relationship of the pulses. Solve the self-representation relationship matrix C through the generalized orthogonal matching pursuit algorithm.

[0011] Step 2: Construct the affinity matrix A based on the self-representation relation matrix C, which is the adjacency matrix representing the topological relationship;

[0012] Step 3: Construct the standard form of the Laplacian matrix corresponding to the adjacency matrix A. Based on the spectral characteristics of the Laplacian matrix, the number of cluster centers k, i.e. the number of radars, is solved by utilizing the "mutation" of the eigenvalue spectrum and the proportion of energy of the smallest eigenvalues.

[0013] Step 4: Take the eigenvectors corresponding to the k smallest eigenvalues ​​in matrix L to form the feature matrix F; select the first k row vectors of the feature matrix F as the initial cluster centers, use the clustering algorithm to cluster each pulse of the radar signal in X, and output the predicted label of each pulse of the radar signal to realize radar signal sorting.

[0014] Furthermore, the specific steps in step 1 for obtaining the time series X of multiple radar signal pulses are as follows:

[0015] X = {x1, x2, ..., x} i ,...,x N}

[0016] Where, x i The pulse description word vector represents the i-th pulse of the radar signal; N represents the number of radar signal pulses;

[0017] The self-representation property of pulse data distributed in the same subspace is that data points in that subspace can be represented by a linear combination of other data points in the same space, specifically:

[0018] X = XC, diag(C) = 0

[0019] Where 0 is the zero vector. The sparse coefficient matrix, also known as the self-representation relation matrix, is formed because it linearly represents the data points originally belonging to this subspace through other data points in this subspace. Therefore, the self-representation relation matrix satisfies the subspace retention property. To solve for the self-representation relation matrix, the above equation can be rewritten as:

[0020]

[0021] Where S is the sparsity, i.e., c i The upper limit of the number of non-zero values; ||·||2 is the l2 norm. ||·||0 is the l0 norm, representing the number of non-zero elements in a vector;

[0022] The generalized orthogonal matching pursuit algorithm is adopted, which uses the similarity between the perception matrix X and the residual r to perform a fixed number of N operations. i Each atom is identified, the support set Λ is expanded, and then the column vectors in the sensing matrix corresponding to the support set are used to complete the sparse signal. Reconstruct and update the residual signal until a specified number of iterations are completed or the residual is less than or equal to the iteration termination threshold ε; where the residual of the first iteration is assumed to be the observation vector x. i ; It is the i-th column of the self-representation relation matrix C.

[0023] Furthermore, in step 2, the affinity matrix A is constructed based on the self-representation relation matrix C, specifically as follows:

[0024] A = |C| + |C T |

[0025] Among them, C T It is the transpose of the self-representation relation matrix C;

[0026] In graph theory, the proximity matrix A is the adjacency matrix representing topological relationships, expressed as:

[0027]

[0028] Among them, a ij This represents the connection weight between the i-th radar signal pulse node and the j-th radar signal pulse node. The larger the weight, the higher the affinity between the two nodes, and the more likely they are to come from the same radar. When the weight is 0, it means that there is no edge connection between the nodes.

[0029] Furthermore, in step 3, the standard form of the Laplacian matrix corresponding to the adjacency matrix A is constructed. Specifically:

[0030] L=DA

[0031]

[0032] Here, the Laplacian matrix is ​​a matrix representing a weighted undirected graph, D is the degree matrix of the weighted undirected graph, and the elements D in matrix D are... pq The degree of each vertex is calculated as follows:

[0033]

[0034] Where p and q are both pulse vertices, deg(v p ) is the sum of the weights of all adjacent edges of the pulse vertex p.

[0035] Furthermore, the method for calculating the number of cluster centers k in step 3 is as follows:

[0036]

[0037] Where σ1,...,σ NLet σ1 ≤ σ2 ≤ … ≤ σ be the eigenvalue spectrum of matrix L arranged in ascending order. N ;a is an arbitrary constant and a>1;

[0038] After initially obtaining the number of cluster centers, the energy proportion of the corresponding number of "minimal" eigenvalues ​​is calculated.

[0039]

[0040] If Ep > τ, then truncate the first N. k = Substitute k eigenvalues ​​back into the formula Perform calculations until Ep ≤ τ; where τ is a preset energy percentage threshold.

[0041] Furthermore, in step 4, the k smallest eigenvalues ​​σ1,...,σ of matrix L are selected. k The corresponding eigenvectors f1,...,f k The characteristic matrix is ​​composed of F, F = (f1, f2, ..., f i ,…,f k The k-means algorithm is used to cluster the pulses of the radar signal in F.

[0042] A computer device / apparatus / system includes a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the radar signal deinterleaving method based on complex network and Laplacian graph clustering described above.

[0043] A computer-readable storage medium having a computer program / instructions stored thereon, which, when executed by a processor, implements the steps of the radar signal deinterleaving method based on complex network and Laplacian graph clustering described above.

[0044] A computer program product includes a computer program / instructions that, when executed by a processor, implement the steps of the radar signal deinterleaving method based on complex network and Laplacian graph clustering described above.

[0045] The beneficial effects of this invention are as follows:

[0046] This invention constructs a complex network from radar pulse data points within the same subspace using the self-representation properties of the data. A generalized orthogonal matching pursuit algorithm is employed to reduce the number of connections between pulses from different radars within the complex network, thereby lowering computational complexity. Borrowing the concept of graph segmentation, Laplace spectral decomposition is used to mine the geometric correlations of radar pulse signals from the same source, enabling efficient sorting of non-ideal radar signals under complex electromagnetic environments. Furthermore, this invention designs an algorithm based on an energy-corrected splitting threshold, which can effectively and accurately determine the number of cluster centers. This invention effectively solves the problem of mis-sorting caused by aliasing or missing parameters of complex radar operating conditions. Attached Figure Description

[0047] Figure 1 This is an example diagram of radar operating status described using pulse descriptor format.

[0048] Figure 2 This is a schematic diagram of the slip modulation of the state parameters.

[0049] Figure 3 This is a schematic diagram of the energy-corrected splitting threshold solution algorithm.

[0050] Figure 4 This is a flowchart illustrating the principle of the present invention.

[0051] Figure 5 This is a data table of radar operating status simulation experiments.

[0052] Figure 6 This is a diagram showing the radar signal sorting accuracy under different jitter ranges when the loss probability is 50%.

[0053] Figure 7 This is a diagram showing the radar signal sorting results under low-dimensional interception parameter scenarios. (a), (c), (e), and (g) represent the sorting results of the SSC-gOMP, RSS-ComNet, SDADPC, and k-means algorithms, respectively, when PA is fixed; (b), (d), (f), and (h) represent the sorting results of the SSC-gOMP, RSS-ComNet, SDADPC, and k-means algorithms, respectively, when DOA is fixed.

[0054] Figure 8 It is the original two-dimensional distribution map of the intercepted radar pulse signal.

[0055] Figure 9 This is a table of radar signal sorting accuracy and ARI data under low-dimensional interception parameter scenarios. Detailed Implementation

[0056] The present invention will now be further described with reference to the accompanying drawings.

[0057] The pulse sequence corresponding to the radar's operating state is a series of ordered radar pulses. In this paper, this series of radar pulses is characterized by multidimensional pulse state parameters (PDWs), where the modulation methods of the five state parameters are not entirely the same. The multi-layer characterization definition of the operating state of a single radar is given below.

[0058] Definition 1: The radar operating state is described by a series of ordered, different state parameters of the radar pulse train. From the perspective of reconnaissance receiver signal processing, the number of pulses N received from a single radar is... l Since the number of state parameters D is finite, the pulse train of a single radar can be expressed as: Each pulse can be characterized by a state parameter.

[0059] Definition 2: Modulation type refers to the different radar operating states generated by controlling state parameters. Common modulation types include fixed, agile, and staggered. To generate different radar operating states, the same state parameter can be loaded with different modulation types. For example, the PRI state parameter can be fixed PRI, Gaussian dithered PRI, staggered PRI, etc.

[0060] Definition 3: Modulation parameters are control parameters for different modulation types of state parameters. For example, the modulation parameters for a slip modulation type include the slip initial value, period, and step size.

[0061] Figure 1 An example of radar operating states described by a pulse descriptor format is given. Each state parameter can be modulated by a different modulation type. M represents the set of modulation types corresponding to the d-th operating state parameter. d The number of corresponding modulation types, The first state parameter of the radar's operating status sample is denoted as pdw, and the corresponding modulation type is slip. M1=5 means that there are 5 modulation types for the state parameter pdw. In this paper, the modulation types of the state parameter include slip, fixed, staggered, agile, and jitter.

[0062] To further describe the concept of modulation parameters, Figure 2 The effects of different modulation parameters on the pdw distribution are shown when the modulation mode is slip. N represents the set of modulation parameters corresponding to the c-th modulation type of the d-th state parameter. c This represents the number of modulation parameters. Different modulation types correspond to different modulation parameters. d=1 indicates that the state parameter in the diagram is pdw, c=1 indicates that the first modulation type of pdw is slip, and N1=3 indicates that the number of slip modulation parameters is 3, including slip initial value, slip period, and slip step size.

[0063] In real-world complex electromagnetic environments, a reconnaissance system simultaneously receives interleaved radar pulse trains composed of radars with unknown state parameters from all radars in the surrounding space. This is essentially a synthesis of multiple radar operating state models, and the interleaved radar operating state model can be represented as:

[0064]

[0065] Where L represents the number of radars in the space where the reconnaissance system is located, and X... l This is the signal from the lth radar.

[0066] Based on the pulse arrival time set by PRI, and using state parameters such as PW, RF, and DOA as characteristic parameters for pulse sorting, the interleaving model of the L-type radar's operating state contains N pulses, which can be rewritten as follows: Where x i This is a multi-dimensional state parameter vector. Multi-parameter radar signal sorting involves separating the pulses from the L radars from the interleaved operating state model of the L radars, and clustering pulses belonging to the same radar.

[0067] x i ={PW i ,RF i DOA i , ...}

[0068] x i This represents the pulse description word vector of the i-th pulse of the radar signal. The elements in the vector include, but are not limited to, PW. i Indicates pulse width, RF i Indicates the carrier frequency, DOA i Indicates arrival time; N is the total number of pulses;

[0069] Inspired by image classification in the field of computer vision, this invention proposes to apply the idea that data of the same category can be well approximated as being distributed in the same low-dimensional subspace. We use the self-representation properties of multi-state parameter pulse signals in the same subspace to represent the affinity relationship.

[0070] The self-representation property of pulse data distributed in the same subspace is that data points in that subspace can be represented by a linear combination of other data points in the same space, specifically:

[0071] X = XC, diag(C) = 0

[0072] Where 0 is the zero vector. It is a sparse coefficient matrix, also known as a self-representation relation matrix, which satisfies the subspace retention property because it is a linear representation of the data points that originally belonged to the subspace through other data points in the subspace.

[0073] Clearly, the above equation is a special form of the compressed sensing model. To further illustrate the similarities between the two, the compressed sensing model is represented as follows:

[0074] X=ΦC

[0075] Where matrix C is sparse, the purpose of compressed sensing is to recover the sparse representation C of the signal from the observed X and the sensing matrix Φ. Therefore, the above equation can be decomposed as:

[0076] min||x i || l ,subject to x i =Xc i

[0077] Among them ||·|| l It is the l-norm, which generally takes the value of 1 or 2 in general problems.

[0078] However, in complex electromagnetic environments, the pulse state parameter distribution during radar signal sorting is unknown and contains a large amount of noise. Furthermore, the sheer number of electromagnetic radiation sources in battlefield environments leads to a large volume of signal data intercepted by reconnaissance receivers, making the aforementioned minimization solution complex and inefficient. Most importantly, in complex electromagnetic spaces, it is impossible to determine whether subspaces are independent or disjoint. Therefore, we can further rewrite the above equation as:

[0079]

[0080] Where S is the sparsity, i.e., c i The upper limit for the number of non-zero values ​​is taken in this paper as between 1% and 2% of the total number of received radar pulses. ||·||2 is the l2 norm, which is... ·||0 is the l0 norm, representing the number of non-zero elements in a vector. For the above problem, this invention uses the Generalized Orthogonal Matching Pursuit (gOMP) algorithm to solve it. The idea of ​​gOMP is to utilize the perception matrix X and the residual r (the residual in the first iteration is assumed to be the observation vector x). i The similarity between the two pairs is fixed at N. i Each atom is identified, the support set Λ is expanded, and then the column vectors in the sensing matrix corresponding to the support set are used to complete the sparse signal. Reconstruct and update the residual signal until the specified number of iterations is completed or the residual is less than or equal to the iteration termination threshold ε, where It is the i-th column of the self-representation relation matrix C.

[0081] This invention can construct an intimacy matrix A = |C| + |C T |, where C TLet A be the transpose of matrix C. In graph theory, the proximity matrix A is the adjacency matrix representing topological relationships, specifically represented as:

[0082]

[0083] Among them, a ij This represents the connection weight between the i-th and j-th radar pulses. The larger the weight, the higher the affinity between the two nodes, and the more likely they are to come from the same radar. When the weight is 0, it means that there is no edge connection between the nodes.

[0084] After obtaining the adjacency matrix, directly using it as input for spectral clustering would result in a large amount of redundant information in the feature vectors. Generally, after obtaining the adjacency matrix A, it needs to be reduced, i.e., removing edges with excessively small weights, to lightweight the complex network while maintaining information integrity and reducing computational complexity. Unlike complex networks built based on global distance, this invention uses the gOMP algorithm for self-representation solving, requiring a sparsity S to be set during initialization, making the complex network inherently lightweight. In this paper, the sparsity S is the number of neighbor connections of a node, generally between 1% and 2% of the total number of received pulses, ensuring that pulses with high global proximity are closely connected.

[0085] Furthermore, in order to determine the number of radiation sources in radar signal sorting, i.e. the number of classification clusters in the clustering problem, this invention utilizes the spectral characteristics of the Laplacian matrix to solve for the number of cluster centers, and proposes a method for solving the number of cluster centers based on energy correction and a split threshold.

[0086] The Laplacian matrix, also known as the Kirchhoff matrix, is a matrix used to represent a weighted undirected graph. The Laplacian matrix and its standard form for the complex network in this invention are as follows:

[0087] L=DA

[0088]

[0089] Where D is the degree matrix of the graph, which is calculated from the degree of each vertex and can be expressed by the following formula:

[0090]

[0091] Among them, deg(v p ) is the sum of the weights of all adjacent edges of vertex p.

[0092] To improve the performance of the clustering algorithm, the initial number of cluster centers can be determined based on the graphical properties of the Laplacian matrix. Solving for the number of cluster centers in the improved sparse subspace clustering algorithm is equivalent to estimating the number of subspaces. Inspired by the estimation of the number of subspaces, the number of subspaces is equal to the standard form of the Laplacian matrix constructed from the proximity matrix A. The number of "minimal" eigenvalues. Ideally, after sorting the eigenvalues ​​from smallest to largest, a "mutation" will occur between two eigenvalues, making the split threshold relatively easy to determine. However, in complex electromagnetic environments, radar signals containing noise and interference can weaken or shift this "mutation," making it easy to erroneously calculate the split threshold. To address these issues, this invention proposes a split threshold calculation algorithm based on energy correction.

[0093] First, the eigenvalues ​​of the standardized Laplacian matrix are... Arrange them in ascending order, i.e., σ1≤σ2≤…≤σ N The number of cluster centers can be estimated by the following formula:

[0094]

[0095] First iteration N k =N, where:

[0096]

[0097] After initially obtaining the number of cluster centers, the energy proportion of the corresponding number of "minimal" eigenvalues ​​is calculated:

[0098]

[0099] If Ep > τ, then truncate the first part. Substitute the eigenvalues ​​back into the formula The calculation continues until Ep ≤ τ, where τ is the energy percentage threshold, which is close to 0 in ideal cases, but is set to 0.2 in the complex electromagnetic case presented in this paper. The specific algorithm for calculating the number of cluster centers based on the energy-corrected split threshold is described in [link to algorithm]. Figure 3 .

[0100] Finally, after obtaining the number of cluster centers k, the feature matrix F can be composed of the eigenvectors corresponding to the k smallest eigenvalues ​​of the Laplace matrix. When the eigenvalues ​​σ of the Laplace matrix... i The corresponding eigenvector is f i When the characteristic matrix F is, it can be expressed as:

[0101] F = (f1, f2, ..., f i ,…,f k )

[0102] Each row in F can be viewed as a sample in a k-dimensional feature space. Radar signal sorting can be achieved by performing k-means clustering on the samples in F. The specific operation of the k-means algorithm is as follows: select the first k row vectors of F as the initial cluster centers; calculate the distance from the remaining sample points to the cluster centers and assign them to the nearest cluster; if the class to which a sample belongs changes, update the cluster center of that class; finally, return k classes, i.e., the predicted label of each pulse. The convergence test of the algorithm uses the sum of squares criterion function.

[0103] To address the problem of low sorting accuracy caused by severe aliasing or missing information in radar signals under complex electromagnetic environments, this invention proposes an improved sparse subspace clustering-based radar signal sorting method, SSC-gOMP. Unlike traditional distance-based clustering algorithms, this method constructs a complex network using the self-representational properties between radar pulse data points. It explores the geometric relationships between radar pulses from the same source from the topological structure of the data points, and uses graph partitioning to perform Laplace spectral clustering on the topological structure. The number of clusters is calculated by analyzing thresholds, thus achieving radar signal sorting under complex electromagnetic environments. This method mainly consists of three parts: constructing the complex network, calculating the number of cluster centers, and spectral clustering. The flowchart of this invention is shown below. Figure 4 As shown.

[0104] Example 1:

[0105] Three multi-functional radars were selected to simulate radar signal interception in a complex electromagnetic environment. Radar 2 has two operating modes, while radars 1 and 3 have three operating modes. Parameter overlap occurs between different radars or different operating modes of the same radar, more closely resembling the signals received by an actual receiver. The operating state parameters of each radar include PW, RF, PRI, DOA, and PA. Each state parameter can employ multiple modulation modes, including fixed, staggered, agile, slip, and jitter. The simulation experimental data for the radar operating states in this embodiment are as follows: Figure 5 As shown. In addition, referring to the general definition of the overlap ratio of a large number of clusters in the field of clustering, that is, an overlap ratio of more than 30% to 50% can usually be considered as a case of large cluster overlap. Therefore, this paper defines the overlap ratio of the parameter feature distribution space as severe aliasing if it exceeds 30%.

[0106] To verify the effectiveness and stability of the method proposed in this patent, this paper uses pulse-level sorting accuracy as a sorting performance evaluation index, which is:

[0107]

[0108] Among them, B i and Let be the true label and cluster label corresponding to the i-th pulse, respectively; N be the total number of radar pulse observations; and δ represent the indication function as follows:

[0109]

[0110] Since the correspondence between the sorting results and the true labels is uncertain, the mapping function `map()` is needed to find the best match between the clustering result labels and the true labels. In this paper, the best match is implemented using the Hungarian algorithm, which can effectively align the clustering result labels with the true labels, thereby calculating the sorting accuracy.

[0111] Furthermore, to compensate for the limitations of sorting accuracy in evaluating clustering results under conditions of random clustering or imbalanced cluster sizes, we add the Adjusted Land coefficient (ARI) as a second evaluation metric. The specific metric is as follows:

[0112]

[0113] Where RI is the Rand coefficient, E[RI] is the expected value of RI, and max(RI) is the maximum value of RI. The formula for calculating RI is as follows:

[0114]

[0115] The relationship between clustering result labels and true labels can be categorized into the following four types:

[0116] a) The true label is e, the clustering result category label is e, and the corresponding number of pulses is represented as TP. e .

[0117] b) If the true label is not e, and the clustering result category label is not e, the corresponding number of pulses is represented as TN. e .

[0118] c) If the true label is e, and the clustering result category label is not e, the number of corresponding pulses is represented as FN. e .

[0119] d) If the true label is not e, but the clustering result class label is e, the number of corresponding pulses is represented as FP. e .

[0120] To verify the sensitivity of the proposed method to pulse jitter, the method was compared with the latest methods ComNet and SDADPC and the traditional algorithm k-means. With a loss probability of 50%, the jitter range was set to [3%, 30%] and the interval to be 3%. The experimental results are as follows: Figure 6As shown in the figure, the sorting accuracy of all four algorithms decreases with increasing jitter, and the method proposed in this patent has the highest sorting accuracy under different jitter levels. This method utilizes self-representation attributes to establish relationships between data points, constructs a complex network to mine the inherent correlations of the same radar signal, and uses spectral clustering to segment the complex topology to complete clustering. Compared with the traditional method of directly inputting the received signal into the k-means algorithm for clustering, the method proposed in this patent is more beneficial for extracting the inherent features of radar pulse signals and can better complete radar signal sorting in complex electromagnetic environments. Although the RSS-ComNet algorithm also mines the correlations of signals by building a complex network, it uses a limited-crossing visible graph algorithm to construct the complex network. When the radar signal parameters are highly jittery, it may prevent the pulse signals of the same radar from establishing connections, or establish incorrect connections, which has a significant impact on the accuracy of radar signal sorting. The SDADPC algorithm loses parameter information during dimensionality reduction, and its accuracy in calculating the number of cluster centers is low when radar signal parameters are severely aliased in complex electromagnetic environments, leading to a decrease in sorting accuracy. In summary, the method proposed in the patent can perform better in radar signal sorting problems under complex electromagnetic environments.

[0121] Example 2:

[0122] In actual radar operating status parameters intercepted, not all parameters can be used as inputs for signal sorting. In the increasingly complex and dense modern electromagnetic environment, receiver gain control, radiating source antenna scanning, and receiver antenna pointing all significantly affect PA measurements. Therefore, pulse amplitude stability is consistently the worst PDW parameter and is sometimes not used as a signal sorting parameter. Furthermore, if the radar radiating sources intercepted by the reconnaissance receiver are far away and may originate from the same direction, resulting in significant overlap of DOA parameters from multiple radars, the DOA parameter is not used as a signal sorting parameter in this case. Based on this, Figure 5 The radar operating state parameters PA and DOA are set to constants to verify the sorting performance of the proposed SSC-gOMP method under low-dimensional interception parameter scenarios.

[0123] The radar sorting experimental results of the algorithm in this paper under fixed PA and DOA state parameters are as follows: Figure 7 As shown in (a) and (b), the experimental results of the comparative algorithms are as follows: Figure 7 As shown in (c)-(h), the distribution of two-dimensional spatial pulse data points is as follows. Figure 8As shown, comparisons reveal that the proposed method outperforms current advanced clustering algorithms when radar signal parameters have low dimensionality. This demonstrates that the SSC-gOMP algorithm, utilizing a complex network built with self-representation properties, can deeply uncover the intrinsic relationships between identical radar data points. In contrast, traditional distance-based sorting algorithms are prone to selecting incorrect cluster centers, leading to widespread clustering errors in radar data points. Figure 7 In (g) and (h), a large number of data points from Radar 1 and Radar 3 were misclassified as Radar 2. The RSS-ComNet algorithm establishes the relationship between each parameter between pulses and constructs a complex network by summing them. Therefore, reducing the parameter dimensionality significantly impacts the algorithm's sorting accuracy. Specific numerical experimental results are as follows... Figure 9 As shown, the sorting accuracy and ARI of the method proposed in this patent are both optimal, further demonstrating the superiority of the method proposed in this patent.

[0124] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A radar signal sorting method based on improved sparse subspace clustering, characterized in that, Includes the following steps: Step 1: Obtain the time series X of multiple radar signal pulses, and use the self-representation properties between multi-state parameter pulse signals in the same subspace to represent the proximity relationship, that is, the spatial correlation relationship of the pulses. Solve the self-representation relationship matrix C through the generalized orthogonal matching pursuit algorithm. Step 2: Construct the affinity matrix A based on the self-representation relation matrix C, which is the adjacency matrix representing the topological relationship; Step 3: Construct the standard form of the Laplacian matrix corresponding to the adjacency matrix A. Based on the spectral characteristics of the Laplacian matrix, the number of cluster centers k, i.e. the number of radars, is solved by utilizing the "mutation" of the eigenvalue spectrum and the proportion of energy of the smallest eigenvalues. Step 4: Take the eigenvectors corresponding to the k smallest eigenvalues ​​in matrix L to form the eigenmatrix F; The first k row vectors of the feature matrix F are selected as the initial cluster centers. The clustering algorithm is used to cluster each pulse of the radar signal in X, and the predicted label of each pulse of the radar signal is output to realize the radar signal sorting.

2. The radar signal sorting method based on improved sparse subspace clustering according to claim 1, characterized in that: The specific steps in step 1 for obtaining the time sequence X of multiple radar signal pulses are as follows: X={x1,x2,…,x i ,…,x N } Where, x i The pulse description word vector represents the i-th pulse of the radar signal; N represents the number of radar signal pulses; The self-representation property of pulse data distributed in the same subspace is that data points in that subspace can be represented by a linear combination of other data points in the same space, specifically: X = XC, diag(C) = 0 Where 0 is the zero vector. The sparse coefficient matrix, also known as the self-representation relation matrix, is formed because it linearly represents the data points originally belonging to this subspace through other data points in this subspace. Therefore, the self-representation relation matrix satisfies the subspace retention property. To solve for the self-representation relation matrix, the above equation can be rewritten as: Where S is the sparsity, i.e., c i The upper limit of the number of non-zero values; ·2 is the l2 norm, • 0 is the l0 norm, representing the number of non-zero elements in the vector; The generalized orthogonal matching pursuit algorithm is adopted, which uses the similarity between the perception matrix X and the residual r to perform a fixed number of N operations. i Each atom is identified, the support set Λ is expanded, and then the column vectors in the sensing matrix corresponding to the support set are used to complete the sparse signal. Reconstruct and update the residual signal until a specified number of iterations are completed or the residual is less than or equal to the iteration termination threshold ε; where the residual of the first iteration is assumed to be the observation vector x. i ; It is the i-th column of the self-representation relation matrix C.

3. The radar signal sorting method based on improved sparse subspace clustering according to claim 1, characterized in that: In step 2, the affinity matrix A is constructed based on the self-representation relation matrix C, specifically as follows: A=C+C T Among them, C T This is the transpose of the self-representation relation matrix C; In graph theory, the proximity matrix A is the adjacency matrix representing topological relationships, expressed as: Among them, a ij This represents the connection weight between the i-th radar signal pulse node and the j-th radar signal pulse node. The larger the weight, the higher the affinity between the two nodes, and the more likely they are to come from the same radar. When the weight is 0, it means that there is no edge connection between the nodes.

4. The radar signal sorting method based on improved sparse subspace clustering according to claim 1, characterized in that: In step 3, the standard form of the Laplacian matrix corresponding to the adjacency matrix A is constructed. Specifically: L=DA Here, the Laplacian matrix is ​​a matrix representing a weighted undirected graph, D is the degree matrix of the weighted undirected graph, and the elements D in matrix D are... pq The degree of each vertex is calculated as follows: Where p and q are both pulse vertices, deg(v p ) is the sum of the weights of all adjacent edges of the pulse vertex p.

5. The radar signal sorting method based on improved sparse subspace clustering according to claim 4, characterized in that: The method for calculating the number of cluster centers k in step 3 is as follows: Where σ1,...,σ N Let σ1 ≤ σ2 ≤ … ≤ σ be the eigenvalue spectrum of matrix L arranged in ascending order. N ;a is an arbitrary constant and a>1; After initially obtaining the number of cluster centers, the energy proportion of the corresponding number of "minimal" eigenvalues ​​is calculated. If Ep > τ, then truncate the first N. k = Substitute k eigenvalues ​​back into the formula Perform calculations until Ep ≤ τ; where τ is a preset energy percentage threshold.

6. The radar signal sorting method based on improved sparse subspace clustering according to claim 1, characterized in that: In step 4, the k smallest eigenvalues ​​σ1,...,σ of matrix L are selected. k The corresponding eigenvectors f1,...,f k The characteristic matrix is ​​composed of F, F = (f1, f2, ..., f i ,…,f k The k-means algorithm is used to cluster the pulses of the radar signal in F.

7. A computer device / equipment / system, comprising a memory, a processor, and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 6.

8. A computer-readable storage medium having a computer program / instructions stored thereon, characterized in that: When the computer program / instructions are executed by the processor, they implement the steps of the method described in any one of claims 1 to 6.

9. A computer program product, comprising a computer program / instructions, characterized in that: When the computer program / instructions are executed by the processor, they implement the steps of the method described in any one of claims 1 to 6.

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